Question

find the value of a and b.​

Answer 1

Answer:

a=13/7. b=9/7

Step-by-step explanation:

(√2+1)^2/3-√2

(2+1+2√2)/3-√2

(3+2√2)/3-√2

by rationalisation

(3+2√2/3-√2)×3+√2/3+√2

(13+9√2)/7

13/7 + 9√2/7. =a+b√2

on compare

a=13/7

b=9/7

Answer 2

$\large{\underline{\underline{\mathfrak{\green{\sf{SOLUTION:-}}}}}}$.

$\large{\underline{\underline{\mathfrak{\sf{Given\:Here:-}}}}}$.

$\large\boxed{\boxed{\frac{(\sqrt{2}+1)^2}{3-\sqrt{2}}\:=\:a\:+\:b\sqrt{2}}}$

$\large{\underline{\underline{\mathfrak{\sf{Find\:here:-}}}}}$.

• Value of a and b

$\large{\underline{\underline{\mathfrak{\sf{Explanation:-}}}}}$.

$\large\boxed{\frac{(\sqrt{2}+1)^2}{3-\sqrt{2}}\:=\:a\:+\:b\sqrt{2}}$

Now , Take L.H.S.

$\implies\frac{(\sqrt{2}+1)^2}{3-\sqrt{2}}$

$\implies\frac{(\sqrt{2})^2+1^2+2(\sqrt{2})}{3-\sqrt{2}}$

$\implies\frac{(2+1+2\sqrt{2}}{3-\sqrt{2}}$

$\implies\frac{(3+2\sqrt{2}}{3-\sqrt{2}}$

Rationalize denominator ,

$\implies\frac{(3+2\sqrt{2})(3+\sqrt{2}}{(3-\sqrt{2})(3+\sqrt{2}}$

$\implies\frac{(9+4+9\sqrt{2}}{9-2}$

$\implies\frac{13+9\sqrt{2}}{7}$

$\implies\frac{13}{7}\:+\frac{9\sqrt{2}}{7}$

Compare to $\:(a+ b\sqrt{2})$

We find here ,

• $\large\boxed{\:a\:=\frac{13}{7}}$

• $\large\boxed{\:b\:=\frac{9}{7}}$

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